In Chapter 2 it is shown that the marginal distribution of plausible values is a consistent estimator of the true latent variable distribution, and, furthermore, that convergence is monotone in an embedding in which the number of items tends to infinity. This result is used to clarify some of the misconceptions that exist about plausible values, and also to show how they can be used in the analyses of educational surveys. Chapter 3 is about two recently published algorithms that can be used to sample from conditional distributions, such as the posterior distribution of ability (i.e. plausible values). It is shown how the efficiency of the two algorithms can be improved when a sample is required from many conditional distributions. Using simulated-data and real-data examples from educational measurement, it is shown how the algorithms can be used to sample from intractable full-conditional distributions of the person and item parameters in an application of the Gibbs sampler. Estimating the structure of networks is a notoriously difficult problem. In Chapter 4 it is shown that using a latent variable representation of the Ising network, it is possible to employ a full data information approach to uncover the network structure, thereby, only ignoring information encoded in the prior distribution (of the latent variables). The full data information approach avoids having to compute the partition function, and is thus computationally feasible, even for networks with many nodes. We illustrate the full data information approach to the estimation of dense networks, thereby complementing recent approaches based on regularization for nearest neighbor networks. In Chapter 5 an example is used to demonstrate that the autocorrelation in MCMC sampling methods using data-augmentation may depend on sample size. This means that, in some cases, the Markov chain will eventually stop mixing when more and more data are observed and thus becomes useless.
|Award date||19 Nov 2014|
|Place of Publication||Enschede|
|Publication status||Published - 19 Nov 2014|